Guid (while it is a valid datatype and class) is NOT a Dataverse column type. There is no such thing as a GUID column in Dataverse (at least, as far as the API is concerned). What you're seeing in SQL is an unfortunate oversimplification of what is actually known as an EntityReference.
I'll elaborate on that before I offer you a solution (but the solution is coming!): in SQL, when you have a Foreign Key you always know what table is being referenced - it is an innate quality of the column itself and so you don't need anything more than the GUID to find the record your FK points to. But Dataverse actually offers more complexity than that. From a single column, you could hypothetically be referencing more than one other table (for example, the OOB Customer lookup points to BOTH Account and Contact).
So, in Dataverse (in plugins) when we are talking about a Foreign Key reference, we don't use the datatype Guid. Instead, we use EntityReference. EntityReference, in turn, has three members, each of which carries some value to us: Id (the Guid), Name (the Primary column, or display name, of the record), and LogicalName (the name of the table where this record is found). The Name attribute is pretty optional - it is really only there for the convenience of developers to reduce the number of API calls we need to make - but the other two are the real identity of the record being referenced.
So, all you need to do to fix your code is change
request.LeadId = new EntityReference("lead", member.GetAttributeValue<Guid>("entityid"));
To
request.LeadId = new EntityReference("lead", member.GetAttributeValue<EntityReference>("entityid").Id);